Problem: Solve for $x$ and $y$ using elimination. ${3x+3y = 30}$ ${-3x-2y = -22}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $3x$ and $-3x$ cancel out. ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {3x+3y = 30}\thinspace$ to find $x$ ${3x + 3}{(8)}{= 30}$ $3x+24 = 30$ $3x+24{-24} = 30{-24}$ $3x = 6$ $\dfrac{3x}{{3}} = \dfrac{6}{{3}}$ ${x = 2}$ You can also plug ${y = 8}$ into $\thinspace {-3x-2y = -22}\thinspace$ and get the same answer for $x$ : ${-3x - 2}{(8)}{= -22}$ ${x = 2}$